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Federated Deep Equilibrium Learning: Harnessing Compact Global Representations to Enhance Personalization

Long Tan Le, Tuan Dung Nguyen, Tung-Anh Nguyen, Choong Seon Hong, Suranga Seneviratne, Wei Bao, Nguyen H. Tran

TL;DR

This work designs a unique model structure featuring an equilibrium layer for global representation extraction, followed by explicit layers tailored for local personalization, and proposes a new FL algorithm rooted in the alternating directions method of multipliers (ADMM), which enables the joint optimization of a shared equilibrium layer and individual personalized layers across distributed datasets.

Abstract

Federated Learning (FL) has emerged as a groundbreaking distributed learning paradigm enabling clients to train a global model collaboratively without exchanging data. Despite enhancing privacy and efficiency in information retrieval and knowledge management contexts, training and deploying FL models confront significant challenges such as communication bottlenecks, data heterogeneity, and memory limitations. To comprehensively address these challenges, we introduce FeDEQ, a novel FL framework that incorporates deep equilibrium learning and consensus optimization to harness compact global data representations for efficient personalization. Specifically, we design a unique model structure featuring an equilibrium layer for global representation extraction, followed by explicit layers tailored for local personalization. We then propose a novel FL algorithm rooted in the alternating directions method of multipliers (ADMM), which enables the joint optimization of a shared equilibrium layer and individual personalized layers across distributed datasets. Our theoretical analysis confirms that FeDEQ converges to a stationary point, achieving both compact global representations and optimal personalized parameters for each client. Extensive experiments on various benchmarks demonstrate that FeDEQ matches the performance of state-of-the-art personalized FL methods, while significantly reducing communication size by up to 4 times and memory footprint by 1.5 times during training.

Federated Deep Equilibrium Learning: Harnessing Compact Global Representations to Enhance Personalization

TL;DR

This work designs a unique model structure featuring an equilibrium layer for global representation extraction, followed by explicit layers tailored for local personalization, and proposes a new FL algorithm rooted in the alternating directions method of multipliers (ADMM), which enables the joint optimization of a shared equilibrium layer and individual personalized layers across distributed datasets.

Abstract

Federated Learning (FL) has emerged as a groundbreaking distributed learning paradigm enabling clients to train a global model collaboratively without exchanging data. Despite enhancing privacy and efficiency in information retrieval and knowledge management contexts, training and deploying FL models confront significant challenges such as communication bottlenecks, data heterogeneity, and memory limitations. To comprehensively address these challenges, we introduce FeDEQ, a novel FL framework that incorporates deep equilibrium learning and consensus optimization to harness compact global data representations for efficient personalization. Specifically, we design a unique model structure featuring an equilibrium layer for global representation extraction, followed by explicit layers tailored for local personalization. We then propose a novel FL algorithm rooted in the alternating directions method of multipliers (ADMM), which enables the joint optimization of a shared equilibrium layer and individual personalized layers across distributed datasets. Our theoretical analysis confirms that FeDEQ converges to a stationary point, achieving both compact global representations and optimal personalized parameters for each client. Extensive experiments on various benchmarks demonstrate that FeDEQ matches the performance of state-of-the-art personalized FL methods, while significantly reducing communication size by up to 4 times and memory footprint by 1.5 times during training.
Paper Structure (16 sections, 4 theorems, 9 equations, 6 figures, 2 tables, 1 algorithm)

This paper contains 16 sections, 4 theorems, 9 equations, 6 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Formulation
  4. Federated Deep Equilibrium Learning
  5. Equilibrium Representation
  6. Forward Pass -- Fixed-Point Iteration
  7. Backward Pass -- Implicit Differentiation
  8. $\textsf{FeDEQ}$: Algorithm Design
  9. Learning Global Representation via ADMM Consensus Optimization
  10. Personalization through Explicit Layers
  11. Convergence Analysis
  12. Experimental Results
  13. Experimental Setup
  14. Main Results
  15. Ablation Study
  16. ...and 1 more sections

Key Result

Lemma 4.2

Suppose $\rho$ is chosen large enough that $\rho > 6L$. After $T$ global iterations since $t$, when all clients have participated in training at least once, we have

Figures (6)

  • Figure 1: The use of explicit and implicit layers as a global representation module for clients in FL. (a) Each client has $M$ explicit layers in its model. (b) Instead of having multiple explicit layers, each client uses only one equilibrium layer parametrized by $\theta_i$.
  • Figure 2: FL using DEQ-MLP with and without $l_\infty$ projection
  • Figure 3: Comparative analysis of model size and test accuracy between $\textsf{FeDEQ}$ and FedRep across various datasets.
  • Figure 4: Comparison of memory usage and training time.
  • Figure 5: Effects of $\rho$ on $\textsf{FeDEQ}$'s convergence.
  • ...and 1 more figures

Theorems & Definitions (5)

  • Lemma 4.2: Decrease in augmented Lagrangian after every $T$ iterations
  • Remark 4.3
  • Lemma 4.4: Lower bound for augmented Lagrangian
  • Theorem 4.5: Convergence of the augmented Lagrangian
  • Theorem 4.6: $\textsf{FeDEQ}$'s convergence